1. Related Rates question 5

Each edge of a cube is expanding at a rate of 4cm/s.

a) How fast is the volume changing when the edge is 5cm?
b) at what rate is the surface area changing when the edge is 7 cm?

2. Originally Posted by math123456
Each edge of a cube is expanding at a rate of 4cm/s.

a) How fast is the volume changing when the edge is 5cm?
b) at what rate is the surface area changing when the edge is 7 cm?

If $s$ is the length of one side of a cube, then its volume is $V=s^3$. We are looking for $\frac{\,dV}{\,dt}$, so that means that $V=s^3\implies\frac{\,dV}{\,dt}=3s^2\frac{\,ds}{\,d t}$

You know the rate at which $s$ is changing, and you know the length of the side at that instant in time. Do you think you can complete the problem now?